Feynman-Kac and Feynman formulas for infinite-dimensional equations with Vladimirov operator

DOI10.1134/S1064562411030070zbMath1251.35181OpenAlexW2033225060MaRDI QIDQ656354

M. Kpekpassi, N. N. Shamarov, O. G. Smolyanov

Publication date: 17 January 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562411030070

zbMATH Keywords

heat-type equationFeynman path integralsVladimirov operator\(p\)-adic spacesPDE on infinite-dimensional spaces

Mathematics Subject Classification ID

Heat equation (35K05) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (8)

Infinite-dimensional evolution equations and the representation of their solutions in the form of Feynman integrals ⋮ Solution of a Cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula ⋮ The Method of Chernoff Approximation ⋮ Chernoff approximation of subordinate semigroups ⋮ Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent ⋮ Функциональный оператор Лапласса на $\mathfrak p$-адическом пространстве и формулы Фейнмана и Фейнмана - Каца ⋮ Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations ⋮ Explicit formula for evolution semigroup for diffusion in Hilbert space

Cites Work

• Unnamed Item
• Feynman formulas for the Schrödinger equations with the Vladimirov operator
• Feynman formulas and path integrals for evolution equations with the Vladimirov operator
• LAGRANGIAN FEYNMAN FORMULAS FOR SECOND-ORDER PARABOLIC EQUATIONS IN BOUNDED AND UNBOUNDED DOMAINS
• One-Parameter Semigroups for Linear Evolution Equations
• POISSON–MASLOV TYPE FORMULAS FOR SCHRÖDINGER EQUATIONS WITH MATRIX-VALUED POTENTIALS

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